Tailoring the light-matter interaction for high-fidelity holonomic gate operations in multiple systems

Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising approach, it often necessitates system-specific adjustments. This work presents a versatile scheme for implementing NHQC gates across multiple qubit systems by optimizing multiple degrees of freedom using a genetic algorithm. The scheme is applied to three qubit systems: ensemble rare-earth ion (REI) qubits, single REI qubits, and superconducting transmon qubits. Numerical simulations demonstrate that the optimized gate operations are robust against frequency detuning and induce low off-resonant excitations, making the scheme effective for advancing fault-tolerant quantum computation across various platforms.